148 research outputs found
Calculation of percolation thresholds in high dimensions for fcc, bcc, and diamond lattices
In a recent article, Galam and Mauger proposed an invariant for site and bond
percolation thresholds, based on known values for twenty lattices (Eur. Phys.
J. B 1 (1998) 255-258). Here we give a larger list of values for more than
forty lattices in two to six dimensions. In this list are new results for fcc,
bcc, and diamond lattices in 4, 5, and 6 dimensions.
The list contains examples of lattices with equal site percolation
thresholds, but different bond percolation thresholds. These and other examples
show that there are deviations from the proposed invariant of up to 12% in two
dimensions, increasing to 69% in higher dimensions.Comment: 12 pages, 3 figures (EPS), LaTe
Site percolation and random walks on d-dimensional Kagome lattices
The site percolation problem is studied on d-dimensional generalisations of
the Kagome' lattice. These lattices are isotropic and have the same
coordination number q as the hyper-cubic lattices in d dimensions, namely q=2d.
The site percolation thresholds are calculated numerically for d= 3, 4, 5, and
6. The scaling of these thresholds as a function of dimension d, or
alternatively q, is different than for hypercubic lattices: p_c ~ 2/q instead
of p_c ~ 1/(q-1). The latter is the Bethe approximation, which is usually
assumed to hold for all lattices in high dimensions. A series expansion is
calculated, in order to understand the different behaviour of the Kagome'
lattice. The return probability of a random walker on these lattices is also
shown to scale as 2/q. For bond percolation on d-dimensional diamond lattices
these results imply p_c ~ 1/(q-1).Comment: 11 pages, LaTeX, 8 figures (EPS format), submitted to J. Phys.
Modifiable factors associated with depression and anxiety in multiple sclerosis
Objectives: Modifiable lifestyle factors are implicated in multiple sclerosis (MS) symptoms but their role in mood is unclear. This study aimed to investigate associations between lifestyle and depression and anxiety in Australian participants with MS.Materials and Methods: Self-reported data from the Australian Multiple Sclerosis Longitudinal Study included the Hospital Anxiety and Depression Scale (HADS) and lifestyle measurements from 1500 participants. SNAP score (range 0-5) was the sum of non-smoking, sufficient fruit/vegetable intake, non-hazardous alcohol consumption, sufficient physical activity and healthy BMI. Analyses by log-binomial and linear regression were adjusted for confounding.Results: Symptoms of depression and anxiety were prevalent in 27% and 40%, respectively; 20% had both. Mean SNAP score was 2.7/5; only 3% met all healthy lifestyle recommendations. Only 10% reported adequate fruit/vegetable intake, and 22% reported a combination of unhealthy BMI, inadequate physical activity and inadequate nutrition. A healthier SNAP score was associated with lower depression prevalence (adjusted prevalence ratio 0.83 [95% CI 0.75, 0.92] per unit increase) and depression severity (adjusted β-0.44 [95% CI -0.64, -0.24]), but not with anxiety.Conclusions: Modifiable lifestyle factors are associated with lower frequency and severity of depression, but not anxiety, in Australian people with multiple sclerosis. The associations between a healthier SNAP score and lower depression are likely bi-directional. SNAP risk factor prevalence and co-occurrence, especially inadequate nutrition and low physical activity, were high among Australians with MS
Burst dynamics during drainage displacements in porous media: Simulations and experiments
We investigate the burst dynamics during drainage going from low to high
injection rate at various fluid viscosities. The bursts are identified as
pressure drops in the pressure signal across the system. We find that the
statistical distribution of pressure drops scales according to other systems
exhibiting self-organized criticality. The pressure signal was calculated by a
network model that properly simulates drainage displacements. We compare our
results with corresponding experiments.Comment: 7 pages, 4 figures. Submitted to Europhys. Let
Critical Percolation in High Dimensions
We present Monte Carlo estimates for site and bond percolation thresholds in
simple hypercubic lattices with 4 to 13 dimensions. For d<6 they are
preliminary, for d >= 6 they are between 20 to 10^4 times more precise than the
best previous estimates. This was achieved by three ingredients: (i) simple and
fast hashing which allowed us to simulate clusters of millions of sites on
computers with less than 500 MB memory; (ii) a histogram method which allowed
us to obtain information for several p values from a single simulation; and
(iii) a new variance reduction technique which is especially efficient at high
dimensions where it reduces error bars by a factor up to approximately 30 and
more. Based on these data we propose a new scaling law for finite cluster size
corrections.Comment: 5 pages including figures, RevTe
Phase Transitions in a Two-Component Site-Bond Percolation Model
A method to treat a N-component percolation model as effective one component
model is presented by introducing a scaled control variable . In Monte
Carlo simulations on , , and simple cubic
lattices the percolation threshold in terms of is determined for N=2.
Phase transitions are reported in two limits for the bond existence
probabilities and . In the same limits, empirical formulas
for the percolation threshold as function of one
component-concentration, , are proposed. In the limit a new
site percolation threshold, , is reported.Comment: RevTeX, 5 pages, 5 eps-figure
Precise determination of the bond percolation thresholds and finite-size scaling corrections for the s.c., f.c.c., and b.c.c. lattices
Extensive Monte-Carlo simulations were performed to study bond percolation on
the simple cubic (s.c.), face-centered cubic (f.c.c.), and body-centered cubic
(b.c.c.) lattices, using an epidemic kind of approach. These simulations
provide very precise values of the critical thresholds for each of the
lattices: pc(s.c.) = 0.248 812 6(5), pc(f.c.c.) = 0.120 163 5(10), and
pc(b.c.c.) = 0.180 287 5(10). For p close to pc, the results follow the
expected finite-size and scaling behavior, with values for the Fisher exponent
(2.189(2)), the finite-size correction exponent (0.64(2)), and
the scaling function exponent (0.445(1)) confirmed to be universal.Comment: 16 pgs, 7 figures, LaTeX, to be published in Phys. Rev.
Determination of the bond percolation threshold for the Kagome lattice
The hull-gradient method is used to determine the critical threshold for bond
percolation on the two-dimensional Kagome lattice (and its dual, the dice
lattice). For this system, the hull walk is represented as a self-avoiding
trail, or mirror-model trajectory, on the (3,4,6,4)-Archimedean tiling lattice.
The result pc = 0.524 405 3(3) (one standard deviation of error) is not
consistent with the previously conjectured values.Comment: 10 pages, TeX, Style file iopppt.tex, to be published in J. Phys. A.
in August, 199
Induction of lymphangiogenesis in and around axillary lymph node metastases of patients with breast cancer
We studied the presence of lymphangiogenesis in lymph node (LN) metastases of breast cancer. Lymph vessels were present in 52 of 61 (85.2%) metastatically involved LNs vs 26 of 104 (25.0%) uninvolved LNs (P<0.001). Furthermore, median intra- and perinodal lymphatic endothelial cell proliferation fractions were higher in metastatically involved LNs (P<0.001). This is the first report demonstrating lymphangiogenesis in LN metastases of cancer in general and breast cancer in particular
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